【摘要】 研究了PDE在数字图像处理方面的应用.从能量分析法切入,构造变分问题,从而得到原始模型;以去噪、提升边缘、保留原图信息为目标改进了原始模型.对于图像处理的难点问题———边缘的去噪去模糊,在文中得到较好的解决.结果表明:经过该方法处理后的图像在提升信噪比方面十分显著,由此建立的扩散模型不仅产生了一种新算法,而且为人们在该领域的后续研究提供了参考.更多还原

【Abstract】 The application of PDE to the digital image process was studied.It began with the method of energy analysis,constructed variational problemes and got the original model.Aimed at noise-removing,edge enhancement and remaining the original image′s information,the original model was improved.The difficulty of image processing-edge′s noise-removing and blur-removing was answered.Result indicated that the image processed by this method was notable in the aspect of SNR enhancement.The function of each PDE′s items was analyzed in image processing from the mathematical view.On the basis of the above analysis,the constructed diffusion model generated the new arithmetic and made reference for the further research in this field.更多还原